Green's functions for chordal SLE curves

• 成果类型: Article
• 署名作者: Rezaei, Mohammad A.; Zhan, Dapeng
• 署名单位: Michigan State University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0802-0
• 发表日期: 2018
• 页码: 1093-1155
• 关键词: schramm-loewner evolution; uniform spanning-trees; erased random-walks; natural parameterization; minkowski content; SCALING LIMITS; intersection

摘要

For a chordal SLE () curve in a domain D, the n-point Green's function valued at distinct points is defined to be here is the Hausdorff dimension of SLE, provided that the limit converges. In this paper, we will show that such Green's functions exist for any finite number of points. Along the way we provide the rate of convergence and modulus of continuity for Green's functions as well. Finally, we give up-to-constant bounds for them.